Int Math 2 Section 9-1
- 2. Section 9-1 Add and Subtract Polynomials
- 3. Essential Questions How do you write polynomials in standard form? How do you add and subtract polynomials? Where you’ll see this: Part-time jobs, travel, geography, modeling
- 4. Vocabulary 1. Monomial: 2. Coefficient: 3. Constant: 4. Polynomial: 5. Term:
- 5. Vocabulary 1. Monomial: An expression that has one term (a number, variable, or a combination of both a number and variables without any addition or subtraction) 2. Coefficient: 3. Constant: 4. Polynomial: 5. Term:
- 6. Vocabulary 1. Monomial: An expression that has one term (a number, variable, or a combination of both a number and variables without any addition or subtraction) 2. Coefficient: The number that is with the variable 3. Constant: 4. Polynomial: 5. Term:
- 7. Vocabulary 1. Monomial: An expression that has one term (a number, variable, or a combination of both a number and variables without any addition or subtraction) 2. Coefficient: The number that is with the variable 3. Constant: A number without a variable 4. Polynomial: 5. Term:
- 8. Vocabulary 1. Monomial: An expression that has one term (a number, variable, or a combination of both a number and variables without any addition or subtraction) 2. Coefficient: The number that is with the variable 3. Constant: A number without a variable 4. Polynomial: A collection of terms that are combined by addition or subtraction 5. Term:
- 9. Vocabulary 1. Monomial: An expression that has one term (a number, variable, or a combination of both a number and variables without any addition or subtraction) 2. Coefficient: The number that is with the variable 3. Constant: A number without a variable 4. Polynomial: A collection of terms that are combined by addition or subtraction 5. Term: Each monomial within a polynomial
- 10. Vocabulary 6. Binomial: 7. Trinomial: 8. Standard Form: 9. Like Terms:
- 11. Vocabulary 6. Binomial: A polynomial with two terms 7. Trinomial: 8. Standard Form: 9. Like Terms:
- 12. Vocabulary 6. Binomial: A polynomial with two terms 7. Trinomial: A polynomial with three terms 8. Standard Form: 9. Like Terms:
- 13. Vocabulary 6. Binomial: A polynomial with two terms 7. Trinomial: A polynomial with three terms 8. Standard Form: When a polynomial is written from highest to lowest degree (highest to lowest exponent) 9. Like Terms:
- 14. Vocabulary 6. Binomial: A polynomial with two terms 7. Trinomial: A polynomial with three terms 8. Standard Form: When a polynomial is written from highest to lowest degree (highest to lowest exponent) 9. Like Terms: Terms that have the same variable parts (variables and exponents)
- 15. Example 1 Tell the variable for which the polynomial is arranged in standard form. 3 2 a. 2a + 3ab − 4b 3 2 b. 2(a + b) + 3(a + b) − 4(a + b) + 7
- 16. Example 1 Tell the variable for which the polynomial is arranged in standard form. 3 2 a. 2a + 3ab − 4b a 3 2 b. 2(a + b) + 3(a + b) − 4(a + b) + 7
- 17. Example 1 Tell the variable for which the polynomial is arranged in standard form. 3 2 a. 2a + 3ab − 4b a 3 2 b. 2(a + b) + 3(a + b) − 4(a + b) + 7 (a + b)
- 18. Example 2 Add the polynomials. 2 2 a. (2x − 3x + 7) + (−2x − 8) + ( x − 7x ) 2 2 2 2 b. (3x − 4 xy ) + (− x + 4 y ) + (2xy − y )
- 19. Example 2 Add the polynomials. 2 2 a. (2x − 3x + 7) + (−2x − 8) + ( x − 7x ) 2 2 2x − 3x + 7 − 2x − 8 + x − 7x 2 2 2 2 b. (3x − 4 xy ) + (− x + 4 y ) + (2xy − y )
- 20. Example 2 Add the polynomials. 2 2 a. (2x − 3x + 7) + (−2x − 8) + ( x − 7x ) 2 2 2x − 3x + 7 − 2x − 8 + x − 7x 2 3x 2 2 2 2 b. (3x − 4 xy ) + (− x + 4 y ) + (2xy − y )
- 21. Example 2 Add the polynomials. 2 2 a. (2x − 3x + 7) + (−2x − 8) + ( x − 7x ) 2 2 2x − 3x + 7 − 2x − 8 + x − 7x 2 3x −12x 2 2 2 2 b. (3x − 4 xy ) + (− x + 4 y ) + (2xy − y )
- 22. Example 2 Add the polynomials. 2 2 a. (2x − 3x + 7) + (−2x − 8) + ( x − 7x ) 2 2 2x − 3x + 7 − 2x − 8 + x − 7x 2 3x −12x −1 2 2 2 2 b. (3x − 4 xy ) + (− x + 4 y ) + (2xy − y )
- 23. Example 2 Add the polynomials. 2 2 a. (2x − 3x + 7) + (−2x − 8) + ( x − 7x ) 2 2 2x − 3x + 7 − 2x − 8 + x − 7x 2 3x −12x −1 2 2 2 2 b. (3x − 4 xy ) + (− x + 4 y ) + (2xy − y ) 2 2 2 2 3x − 4 xy − x + 4 y + 2xy − y
- 24. Example 2 Add the polynomials. 2 2 a. (2x − 3x + 7) + (−2x − 8) + ( x − 7x ) 2 2 2x − 3x + 7 − 2x − 8 + x − 7x 2 3x −12x −1 2 2 2 2 b. (3x − 4 xy ) + (− x + 4 y ) + (2xy − y ) 2 2 2 2 3x − 4 xy − x + 4 y + 2xy − y 2 2 2x − 2xy + 3y
- 25. Example 3 Subtract 4x + y from the sum of x + 3y and 8x - 2y.
- 26. Example 3 Subtract 4x + y from the sum of x + 3y and 8x - 2y. ( x + 3y ) + (8 x − 2y ) − (4 x + y )
- 27. Example 3 Subtract 4x + y from the sum of x + 3y and 8x - 2y. ( x + 3y ) + (8 x − 2y ) − (4 x + y ) x + 3y + 8 x − 2y − 4 x − y
- 28. Example 3 Subtract 4x + y from the sum of x + 3y and 8x - 2y. ( x + 3y ) + (8 x − 2y ) − (4 x + y ) x + 3y + 8 x − 2y − 4 x − y 5x
- 29. Example 4 Simplify. 3 2 3 2 a. (6 x + 3x − 11x ) + (2x − 9 x − 5 x ) 2 2 2 2 b. ( x y − 2xy + 8) − (−7x y + 2xy − 4)
- 30. Example 4 Simplify. 3 2 3 2 a. (6 x + 3x − 11x ) + (2x − 9 x − 5 x ) 3 2 3 2 6 x + 3x − 11x + 2x − 9 x − 5 x 2 2 2 2 b. ( x y − 2xy + 8) − (−7x y + 2xy − 4)
- 31. Example 4 Simplify. 3 2 3 2 a. (6 x + 3x − 11x ) + (2x − 9 x − 5 x ) 3 2 3 2 6 x + 3x − 11x + 2x − 9 x − 5 x 3 2 8 x − 6 x − 16 x 2 2 2 2 b. ( x y − 2xy + 8) − (−7x y + 2xy − 4)
- 32. Example 4 Simplify. 3 2 3 2 a. (6 x + 3x − 11x ) + (2x − 9 x − 5 x ) 3 2 3 2 6 x + 3x − 11x + 2x − 9 x − 5 x 3 2 8 x − 6 x − 16 x 2 2 2 2 b. ( x y − 2xy + 8) − (−7x y + 2xy − 4) 2 2 2 2 x y − 2xy + 8 + 7x y − 2xy + 4
- 33. Example 4 Simplify. 3 2 3 2 a. (6 x + 3x − 11x ) + (2x − 9 x − 5 x ) 3 2 3 2 6 x + 3x − 11x + 2x − 9 x − 5 x 3 2 8 x − 6 x − 16 x 2 2 2 2 b. ( x y − 2xy + 8) − (−7x y + 2xy − 4) 2 2 2 2 x y − 2xy + 8 + 7x y − 2xy + 4 2 2 8 x y − 4 xy + 12
- 34. Example 4 Simplify. 2 2 2 2 2 c. ( x y + x − xy ) − (− y + y + xy + 4 x y )
- 35. Example 4 Simplify. 2 2 2 2 2 c. ( x y + x − xy ) − (− y + y + xy + 4 x y ) 2 2 2 2 2 x y + x − xy + y − y − xy − 4 x y
- 36. Example 4 Simplify. 2 2 2 2 2 c. ( x y + x − xy ) − (− y + y + xy + 4 x y ) 2 2 2 2 2 x y + x − xy + y − y − xy − 4 x y 2 2 2 −3x y + x − 2xy + y − y
- 37. Problem Set
- 38. Problem Set p. 378 #1-39 odd “Deeds, not stones, are the true monuments of the great.” - John L. Motley